This paper motivates and develops a nonlinear extension of the Vector
Autoregressive model which we call the Vector Floor and Ceiling model. Bayesian and
classical methods for estimation and testing are developed and compared in the context of
an application involving U.S. macroeconomic data. In terms of statistical significance both
classical and Bayesian methods indicate that the (Gaussian) linear model is inadequate.
Using impulse response functions we investigate the economic significance of the statistical
analysis. We find evidence of strong nonlinearities in the contemporaneous relationships
between the variables and milder evidence of nonlinearity in the conditional mean.